God help a total nob with bevel
Bevel will not work correctly on geometry with vertices too close to each other. Either it will overlap awfully if beveling without clamping or as you discovered there won't be any overlaps with Clamp Overlap but bevel effect will be almost invisible. 

There are ways to work this around - either retopo the mesh using any of existing ways so far (manually or using any created solutions be it addons or other programs) or build bevel using curves possibilities.



To go with curves first selected vertices of the butterfly profile were duplicated and separated into another object (P > By Selection). Then that object was converted to curve via Alt+C in Object mode. Curve was cleaned in Edit mode afterwards - type of splines was set to Bezier, handles - to Auto so that shape is smoothed by default as much as possible.

Next step was to extrude and bevel the curve object. Easiest way is to set curve type to 2D in curve object settings, Fill option to Both and Extrude to something other than 0, depending on desired depth.



However if beveling intersections appear in the corners where curve handles are too near to each other due to details. 



One way to compensate that is to decrease Offset value to the same amount as Bevel was set to, but negative. In this case Bevel was set 0.5 and the Offset to -0.5.



Some extra curve handles in the corners were removed and others were adjusted to get rid of remaining overlaps.